Question

In order to study the effectiveness of a training program, president kirkman randomly picks 5 employees and records the respective time taken in assembling part k. of the times are 8, 7, 9, 6, and 10 minutes, what is the standard deviation

Answer 1

Answer: The standard deviation of the sample is 1.58.

We calculate the standard deviation as follows:

Let time taken by employees be t

Let the Mean time (average) taken by employees be $\overline{t}$

               t                   t - $\overline{t}$     (t - $\overline{t}$ )²

              8                     $8-8 = 0$                   $0^{2} = 0$

               7                     $7-8 = -1$                  $-1^{2} = 1$    

              9                      $9-8 = 1$                   $1^{2} = 1$

              6                     $6-8 = -2$                 $-2^{2} = 4$

             10                     $10-8 = 2$                 $2^{2} = 4$

Total     40                                                                              10      

We find the mean or average as follows:

$\overline{t} = \frac{\sum t}{N}$

$\overline{t} = \frac{40}{5}$

$\overline{t} = 8$

The formula for calculating the standard deviation of a sample is:

$\sigma_{s} = \sqrt{\frac{\sum (t-\overline{t})^{2}}{N-1}}$

$\sigma_{s} = \sqrt{\frac{10}{5-1}}$

$\sigma_{s} = \sqrt{\frac{10}{4}}$

$\sigma_{s} = 1.58113883$